The polynomial is [tex](x^{3})-(5x^{2} )-9x+45[/tex].
Polynomial:
- A polynomial is a mathematical expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
- It is made up of indeterminates (also known as variables) and coefficients.
- [tex]x^{2} -4x+7[/tex] is an illustration of a polynomial with a single indeterminate [tex]x[/tex].
- Three-variable example: [tex]x^{3} +2xyz^{2} -yz+1[/tex].
- Numerous branches of mathematics and science use polynomials.
- For instance, they are used to define polynomial functions, which show up in contexts ranging from basic chemistry and physics to economics and social science, and they are used in calculus and numerical analysis to approximate other functions.
Solution -
[tex](x-3)(x+3)(x-5)\\(x^{2} -9)(x-5)\\(x^{3} )-(5x^{2} )-9x+45[/tex]
Therefore, the polynomial is [tex](x^{3})-(5x^{2} )-9x+45[/tex].
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